Solve for x : 3^x =2x+2 Mastermind


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Question Number 170946 by Mastermind last updated on 04/Jun/22

$Solve for x :$ $3^{x} = 2 x + 2$ $Mastermind$
	Answered by mr W last updated on 04/Jun/22
	$3^x =2(x+1) 3^(x+1) =6(x+1) e^((x+1)ln 3) =6(x+1) −(x+1)ln 3 e^(−(x+1)ln 3) =−((ln 3)/6) −(x+1)ln 3=W(−((ln 3)/6)) ⇒x=−1−(1/(ln 3))W(−((ln 3)/6))= { ((1.444561)),((−0.790109)) :}$
	$3^{x} = 2 (x + 1)$ $3^{x + 1} = 6 (x + 1)$ $e^{(x + 1) \ln 3} = 6 (x + 1)$ $- (x + 1) \ln 3 e^{- (x + 1) \ln 3} = - \frac{\ln 3}{6}$ $- (x + 1) \ln 3 = W (- \frac{\ln 3}{6})$ $\Rightarrow x = - 1 - \frac{1}{\ln 3} W (- \frac{\ln 3}{6}) = {\begin{cases} 1.444561 \\ - 0.790109 \end{cases}$
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